Algebra II
Hong Kong
Stage 1 - Stage 3
Factorising the HCF
Lesson
We've previously learnt how to factorise both algebraic and numeric terms from expressions. Now we are going to look at expressions where the highest common factor (HCF) may consist of more than one pronumeral, or even a linear factor. Let's look at some examples below.
Example 1
Factorise $6pqr+18pqz$6pqr+18pqz
| $6p^2qr+18pqz$6p2qr+18pqz | $=$= | $6\left(p^2qr+3pqz\right)$6(p2qr+3pqz) Take out the highest numerical factor |
| $=$= | $6pq\left(pr+3z\right)$6pq(pr+3z) Take out the highest common powers of each pronumeral |
Since there was a $q$q present in both terms, as well as a single power of $p$p, we were able to pull both of these out of the expression as factors.
More examples
Question 1
Factorise the following expression by taking out the highest common factor:
$9x^2y^2z-18xyz$9x2y2z−18xyz
Question 2
Factorise the following expression:
$pqr+p^2q^2r+p^3q^3r$pqr+p2q2r+p3q3r
Question 3
Factorise $6r^3tv+9r^2t^2v^3-12rt^3v^2$6r3tv+9r2t2v3−12rt3v2.